Table Of ContentHα as a Luminosity Class Diagnostic for K- and M-type Stars
Jeff Jennings1 and Emily M. Levesque2
ABSTRACT
6
1
0
2 We have identified the Hα absorption feature as a new spectroscopic diagnos-
r tic of luminosity class in K- and M-type stars. From high-resolution spectra of 19
a
M stars with well-determined physical properties (including effective temperatures
and stellar radii), we measured equivalent widths for Hα and the Ca II triplet
2
and examined their dependence on both luminosity class and stellar radius. Hα
]
R shows a strong relation with both luminosity class and radius that extends down
S to late M spectral types. This behavior in Hα has been predicted as a result
.
h of the density-dependent overpopulation of the metastable 2s level in hydrogen,
p
- an effect that should become dominant for Balmer line formation in non-LTE
o
r conditions. We conclude that this new metallicity-insensitive diagnostic of lumi-
t
s nosity class in cool stars could serve as an effective means of discerning between
a
[ populations such as Milky Way giants and supergiant members of background
2 galaxies.
v
5
7
5
7 1. Introduction
0
.
1
Luminosity class diagnostics are critically important for the study of cool (K- and M-
0
6 type) stars both in and beyond the Milky Way. An effective luminosity class discriminant
1
: is necessary in order to distinguish between foreground dwarf and giant populations and
v
i background supergiants, particularly when studying massive star populations in neighboring
X
Local Group galaxies. Massey (1998) illustrated this, determining that ∼50% of the red
r
a stars included in the Humphreys & Sandage (1980) survey of M33 were actually foreground
dwarfs rather than red supergiant members of M33. In this case, the foreground dwarf
and background supergiant populations were separated by the use of a (B−V) vs. (V −R)
color-color diagram, which revealed a clear separationin (B−V) as a consequence of surface-
gravity-dependent line blanketing effects. However, while this color-based method can be
1CASA,DepartmentofAstrophysicalandPlanetarySciences,UniversityofColorado,389-UCB,Boulder,
CO 80309,USA
2Department of Astronomy, University of Washington, Seattle, WA 98195, USA
Corresponding author: [email protected]
– 2 –
useful for separating stars at extreme ends of the luminosity class regime, delving into a more
precise distinction between dwarf, giant, and supergiant requires the increased precision of
spectroscopic diagnostics.
Absorption features of neutral and singly-ionized metal lines are commonly cited as
luminosity class diagnostics in cool stars (e.g. Keenan & Hynek 1945, Rayner et al. 2009,
Negueruela et al. 2012). These include the strong Ca I, Mg I, and Na D absorption features
(e.g. Smith & Drake 1987, Fuhrmann et al. 1997), but the most well-studied is the Ca II
triplet (8498, 8542, 8662˚A). This absorption feature has been shown to be strongly sensitive
tosurfacegravity, withthethreeabsorptionlinesallgettingstrongeratlowersurfacegravities
(see Cenarro et al. 2001a,b and references therein). This relation has been used to identify
supergiants both in the Milky Way and in Local Group galaxies (e.g. Garzon et al. 1997;
Mantegazza 1992; Massey 1998; Rayner et al. 2009; Negueruela et al. 2012; Britavskiy et al.
2014, 2015).
Unfortunately there are several drawbacks to using the Ca II triplet as a means of
distinguishing between dwarfs, giants, and supergiants, particularly across multiple host
galaxies. The Ca II triplet feature is sensitive to metallicity (e.g. Armandroff & Da Costa
1991, Battaglia et al. 2008, Starkenburg et al. 2010, Sakari & Wallerstein 2016). While
this effect is small compared to luminosity class effects between dwarfs and supergiants (e.g.
Mallik 1997, Massey 1998), it can lead to difficulties distinguishing between intermediate
classes, such as dwarfs and giants or giants and supergiants. As an example, Massey (1998)
noted that low-metallicity supergiants and solar-metallicity giants have comparable equiva-
lent widths. Thisambiguityintroduces thepossibilityofconfusingforegroundMilkyWayred
giants with lower-metallicity background red supergiants, a common scenario when trying
to separate halo giants from background supergiant populations of metal-poor Local Group
galaxies such as the Magellanic Clouds, NGC 6822, and WLM (e.g. Levesque et al. 2006,
2007; Levesque & Massey 2012; Britavskiy et al. 2014, 2015). In addition, the Ca II triplet’s
sensitivity to luminosity class has not been calibrated for spectral types later than M4 (e.g.
Negueruela et al. 2012), and observations show evidence that this relation may break down
beyond earlyM spectral types (e.g. Rayner et al. 2009). Finally, the Ca IItriplet lines canbe
contaminated by the hydrogen Paschen lines; while this contamination is corrected for in the
Cenarro et al. (2001a) calibration of the Ca II triplet index with luminosity class, in practice
it is often difficult to distinguish between these features in observations (e.g. Britavskiy et
al. 2014).
Here we present an examination of Ca II triplet and Hα absorption features in a sample
of 19 K- and M-type dwarfs, giants, and supergiants. We drew our sample from stars with
pre-determined effective temperatures and stellar radii and acquired new high-resolution
– 3 –
(R ∼ 31500) spectra (Section 2). From these spectra and the stars’ previously-determined
physical properties we were able to measure the equivalent widths of both features and
examine their dependence on both luminosity class and radius. In addition to confirming
previous work on the Ca II triplet, we also find that the Hα absorption feature serves as an
excellent diagnostic of both luminosity class and radius in stars extending down to late M
spectral types (Section 3), a result of density-dependent overpopulation of the metastable
2s level in hydrogen. We consider the results’ implications and potential applications for
future work, particularly in discerning between foreground giant and background supergiant
populations (Section 4).
2. Observations
2.1. Sample Selection and Observations
Our sample has been drawn principally from van Belle et al. (1999, 2009a, 2009b), who
presentedinterferometrically-determined radiiandeffectivetemperatures(T )forcooldwarf
eff
(class V), giant (III), and supergiant (I) stars. These “direct” radii determinations combined
with thewell-known natureof thesamples (i.e., precise metallicities for thedwarfs andgiants
where metallicity evolution may be substantial and distances to host OB associations for the
supergiants) make them an ideal resource for testing luminosity class diagnostics. From
these studies, along with three additional cool stars with precisely determined T values
eff
from Cenarro et al. (2001a), we have a sample of 19 stars.
To avoid confusing luminosity class effects with T -dependent changes in line strengths,
eff
we split our sample into four discrete bins according to previously-determined T : 3580 K,
eff
3650 K, 4050 K, and 4150 K. Bin identifiers are the mean T of each bin rounded to the
eff
nearest 10 K; stars within each bin span a total range of ≤50 K. Changes in spectral features
with luminosity class were then compared within each bin. Our full sample, sorted by bins,
is given in Table 1.
We observed our sample of cool stars using the Astrophysics Research Consortium
Echelle Spectrograph (ARCES; Wang et al. 2003) on the Apache Point Observatory 3.5-
meter telescope, using the default 1′′.6 × 3′′.2 slit for an R ∼ 31500. On 2014 July 29 we
observed 11 targets under clear conditions with a seeing of 1′′.1; on 2015 February 5 we ob-
served 8 targets under clear conditions with a seeing of 1′′.0. To achieve precise flatfield and
wavelength calibrations for each star, we observed quartz lamps and ThAr lamps, as well as
– 4 –
telluric standards. The spectra were reduced using standard IRAF1 procedures, using the
ThAr lamp spectra for wavelength calibrations.
3. Equivalent Widths and Analyses
We measured the equivalent widths of the Ca II triplet (summing the three lines, here-
after W(CaT); Mallik 1997, Cenarro et al. 2001a) and the Hα line (hereafter W(Hα)) using
IRAF. We found that Voigt profiles yielded the best fits to the absorption features (see also
Sakari & Wallerstein 2016 for a discussion of Ca II triplet line profiles), with a systematic
measurement error of ∼1%; our W(CaT) values show good agreement with those measured
by Mallik (1997) and Massey (1998). Table 1 includes measured W(CaT)and W(Hα) values
for each star in our sample.
The star HD 207991 was originally included in our sample as a supergiant star of lu-
minosity class I, based on the spectral type reported in van Belle et al. (2009b); however,
both the radius measured in van Belle al. (2009b) and our measured equivalent widths are
more consistent with the star being a class III rather than a class I. Van Belle et al. (2009b)
specifically singles out this star as being unusually small for a supergiant and suggests that it
may be misclassified. Furthermore, the original reference for the spectral type of HD 207991,
Keenan & McNeil (1989), classifies it as a K4 III star. Based on this we classify HD 207991
here as a giant with luminosity class III.
3.1. The Dependence of Hα On Luminosity Class
While the dependence of W(CaT) on luminosity has been previously studied in cool
stars (e.g. Cenarro et al. 2001a), this is the first study of such behavior in W(Hα). The
effect is a predicted consequence of the density-dependent overpopulation of the metastable
2s level in hydrogen, first described in detail in Struve et al. (1939) and further discussed in
Huang et al. (2012). Struve et al. (1939) posit that observations of strong Balmer absorption
lines in late type supergiants may be explained by the metastability of hydrogen’s 2s state,
a consequence of the classically forbidden 2s → 1s radiative transition. They suggest that
measurements of the Paschen lines may confirm this, with the expectation that the widths of
these lines, originating from the n = 3 level (i.e., states that are not metastable), would not
1IRAFisdistributedbyNOAO,whichisoperatedbyAURA,Inc.,undercooperativeagreementwiththe
NSF.
– 5 –
show the broadening observed for Hα. Huang et al. (2012) measure the equivalent widths
of Paschen delta (Pδ) and Hα for G-type and later stars, observing Pδ widths consistent
with model spectra that assume LTE. By contrast, they observe substantially broader Hα
widths than predicted under LTE and note that because of the forbidden 2s → 1s transition,
the population of the metastable 2s level in non-LTE is largely determined by radiative and
collisionaltransitionswithotherexcitedstates. Inlowdensityconditionswherethemeanfree
path is larger (such as the atmospheres of cool giant and supergiant stars with lower surface
gravities) such transitions are less frequent, leading to an overpopulation of the metastable
2s state. This effect in cool, late type stars should then scale inversely with surface gravity
and, consequently, luminosity class, resulting in an Hα line width that increases as we move
from class V giants to class I supergiants. This is consistent with our observations, as shown
in Figure 1.
TheevolutionofW(Hα)isconsistentacrossourT bins, supportingthenotionthatthis
eff
overpopulation effect dominates temperature effects for both K- and M-stars (in agreement
with Struve et al. 1939 and Huang et al. 2012). A connection between luminosity class and
the strength of the Hα line has also been observed in narrow-band survey photometry (e.g.
Drew et al. 2005, 2014; Wright et al. 2008).
3.2. A Comparison of Luminosity Class Diagnostics
Figure 2 compares W(CaT) to luminosity class (top) and stellar radius (bottom) for
stars in each of our four T bins. As seen in previous work, W(CaT) shows a clear relation
eff
with luminosity class, with a mean fractional difference between classes I and V across T
eff
bins of −0.80. We do, however, see that this relation weakens at lower T (in the 3580 K
eff
bin the piecewise relation shows much better agreement than the relatively poor linear fit as
a consequence of the inability to clearly distinguish between giants and supergiants). This is
in agreement with the results of Rayner et al. (2009) and Negueruela et al. (2012) suggesting
that the W(CaT)-luminosity class relation breaks down beyond early M spectral types (3580
K corresponds to a spectral type of M3-3.5 in supergiants; Levesque et al. 2005).
Figure 3 illustrates the same comparisons to luminosity class and stellar radius for
W(Hα). We see that the W(Hα) feature shows a comparable relation with luminosity class,
yielding a mean fractional difference between classes I and V of −1.00. This persists in all
four T bins, ranging from −0.83 in the 4050 K bin to −1.43 in the 3580 K bin.
eff
The relation between these spectral features and stellar radius is harder to quantify;
however, we expect the behavior of W(CaT) and W(Hα) to be inversely dependent on
– 6 –
surface gravity, with W ∝ R2. The small sample sizes preclude any possibility of a robust
polynomial fit within any single bin. We instead normalize the data points in each bin and
combine thefulldataset todeterminebest-fit second-order polynomialsforboththeW(CaT)
and W(Hα) relations. As illustrated in Figure 4, we find that while a ∼ R2 relation offers
the best fit for both datasets (as opposed to linear, exponential, or higher-order fits), the fit
is better for the W(Hα) data with a lower residual standard deviation (17% for W(Hα) as
opposed to 25% for W(CaT)).
4. Discussion
From our analyses of high-resolution spectra for 19 K- and M-type stars, we have iden-
tified W(Hα) as a new diagnostic of luminosity class and radius in cool stars. This agrees
with predictions stating the density-dependent overpopulation of the metastable 2s level
hydrogen should become a dominant effect in non-LTE conditions, leading to a broadening
of Hα at lower surface gravities (Struve et al. 1939, Huang et al. 2012).
Reliable spectroscopic diagnostics of luminosity class for cool stars are particularly valu-
able in the current era of extragalactic stellar spectroscopy. Contamination of extragalactic
red supergiant samples by foreground dwarfs can be mitigated through the use of color-
color diagrams (Massey 1998); however, distinguishing between background supergiants and
foreground giants can only be done through spectroscopic analyses. The utility of W(CaT)
in discerning between giants and supergiants is limited. Differences in metallicity between
the foreground and background populations can complicate interpretation of the Ca II line
widths, and contamination by the nearby Paschen lines in both absorption and, in some
cases, emission (see, for example, Castelaz et al. 2000, Levesque et al. 2014) makes the
equivalent widths harder to measure. At the coolest temperatures we also find that the
W(CaT) relation with luminosity class becomes less pronounced when comparing giants and
supergiants.
By comparison, W(Hα) is a good diagnostic of luminosity class across the full range
of temperatures represented in our sample and should be independent of metallicity effects.
The robust relation between W(Hα) and stellar radius suggests this feature does indeed
scale as expected for a direct tracer of luminosity and that it is a more effective tracer
than W(CaT). While Hα is certainly a weaker spectral feature than the Ca II triplet for
K- and M-type stars, high-resolution observations of either feature are still required for use
as luminosity diagnostics; acquiring sufficiently high-S/N and high-resolution observations
of Hα is attainable for populations extending out to extragalactic supergiants in the Local
Group.
– 7 –
The applications of W(Hα) as a luminosity class diagnostic may also extend to earlier
spectraltypes; Huangetal.(2012)notethatthenon-LTEeffectsobserved hereinHαarealso
expected in G-type stars. Extending this analysis to G and possibly even F-type stars would
be useful for identifying the temperature limits of this phenomenon and could be extremely
valuable for the study of extragalactic yellow supergiant populations. For these warmer stars
separating background class I and foreground class III and V stars is particularly challenging
due to a lack of color-color diagnostics and Paschen line contamination of the Ca II triplet
(see Neugent et al. 2010, 2012); the strong Balmer absorption features in these populations
could offer a compelling alternative diagnostic. Finally, future work studying W(CaT) and
W(Hα) for a larger sample of well-studied Galactic K- and M-type stars will allow us to
quantify the relation between these spectroscopic features and stellar properties such as
mass, metallicity, radius, and surface gravity to much greater precision.
This paper is based on data gathered with the Apache Point Observatory 3.5-meter
telescope, which is owned and operated by the Astrophysical Research Consortium. We
gratefully acknowledge the unparalleled expertise of George Wallerstein shared during con-
versations related to this work, as well as useful discussions with Adam Ginsburg, David
Pitman, and Allison Youngblood. Helpful comments by the referee, Philip Massey, have
improved the presentation of our arguments in several places. JJ thanks C. Davis for her
guidance. JJ was supported in part by an Undergraduate Research Opportunities Program
Research Assistantship from the University of Colorado. EML was supported in part by
NASA through Hubble Fellowship grant number HST-HF-51324.01-A from the Space Tele-
scope Science Institute, which is operated by the Association of Universities for Research in
Astronomy, Incorporated, under NASA.
REFERENCES
Armandroff, T. E. & Da Costa, G. S. 1991, AJ, 101, 1329
Battaglia, G., Irwin, M., Tolstoy, E., Hill, V., Helmi, A., Letarte, B., & Jablonka, P. 2008,
MNRAS, 383, 183
Britavskiy, N. E., Bonanos, A. Z., Mehner, A., Garcia-Alvarez, D., Prieto, J. L., & Morrell,
N. I. 2014, A&A, 562, A75
Britavskiy, N. E., Bonanos, A. Z., Mehner, A., Boyer, M.L., & McQuinn, K. B. W. 2015,
A&A, 584, A33
Castelaz, M. W., Luttermoser, D. G., Caton, D. B., & Piontek, R. A. 2000, AJ, 120, 2627
Cenarro, A.J., Cardiel, N., Gorgas, J., Peletier, R. F., Vazdekis, A., & Prada, F. 2001a,
– 8 –
MNRAS, 326, 959
Cenarro, A. J., Gorgas, J., Cardiel, N., Pedraz, S., Peletier, R. F., & Vazdekis, A. 2001b,
MNRAS, 326 981
Drew, J. E., Greimel, R., Irwin, M. J., et al. 2005, MNRAS¡ 362, 753
Drew, J. E., Gonzalez-Solares, E., Greimel, R., et al. 2014, MNRAS, 440, 2036
Fuhrmann, K., Pfeiffer, M., Frank, C., Reetz, J., & Gehren, T. 1997, A&A, 323, 909
Garzon, F., Lopez-Corredoira, M., Hammersley, P., Mahoney, T. J., Calbet, X., & Beckman,
J. E. 1997, ApJ, 491, L31
Gustafsson, B., Edvardsson, B., Eriksson, K., Jorgensen, U. G., Nordlund, A., & Plez, B.
2008, A&A, 486, 951
Huang, W., Wallerstein, G., & Stone, M. 2012, A&A, 547, A62
Humphreys, R. M. & Sandage, A. 1980, ApJS, 44, 319
Keenan, P. C. & Hynek, J. A. 1945, ApJ, 101, 265
Keenan, P. C. & McNeil, R. C. 1989, ApJS, 71, 245
Levesque, E. M., Massey, P., Olsen, K. A. G., Plez, B., Josselin, E., Maeder, A., & Meynet,
G. 2005, ApJ, 628, 973
Levesque, E. M., Massey, P., Olsen, K. A. G., Plez, B., Josselin, E., Maeder, A., & Meynet,
G. 2006, ApJ, 645, 1102
Levesque, E. M., Massey, P., Olsen, K. A. G., & Plez, B. 2007, ApJ, 667, 202
Levesque, E. M. & Massey, P. 2012, AJ, 144, 2
Levesque, E. M., Massey, P., Z˙ytkow, A. N., & Morrell, N. 2014, MNRAS, 443, L94
Mallik, S. V. 1997, A&AS, 124, 359
Mantegazza, L. 1992, A&A, 265, 527
Massey, P. 1998, 501, 153
Negueruela, I.,Marco, A.,Gonzalez-Fernandez, C.,Jimenez-Esteban, F.,Clark, J.S.,Garcia,
M., & Solano, E. 2012, A&A, 547, A15
Neugent, K. F., Massey, P., Skiff, B., Drout, M. R., Meynet, G., & Olsen, K. A. G. 2010,
ApJ, 719, 1784
Neugent, K. F., Massey, P., Skiff, B., & Meynet, G. 2012, ApJ, 749, 177
Park, S., Kang, W., Lee, J., & Lee, S. 2013, AJ, 146, 73
Rayner, J. T., Cushing, M. C., & Vacca, W. D. 2009, ApJS 185, 289
– 9 –
Sakari, C. M. & Wallerstein, G. 2016, MNRAS, 456, 831
Smith, G. & Drake, J. J. 1987, A&A, 181, 103
Starkenburg, E., Hill, V., Tolstoy, E., et al. 2010, A&A, 513, 34
Struve, O., Wurm, K., & Henyey, L. G. 1939, PNAS, 25, 67
van Belle, G. T., Lane, B. F., Thompson, R. R., et al. 1999, AJ, 117, 521
van Belle, G. T. & von Braun, K. 2009a, ApJ, 694, 1085
van Belle, G. T., Creech-Eakman, M. J., & Hart, A. 2009b, MNRAS, 394, 1925
Wang, S., Hildebrand, R. H., Hobbs, L. M., et al. 2003, SPIE, 4841, 1145
Wright, N. J., Greimel, R., Barlow, M. J., et al. 2008, MNRAS, 390, 929
This preprint was prepared with the AAS LATEX macros v5.2.
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Table 1. Program Stars and Equivalent Widths
Star Luminosity Teff Radius W (˚A) Refsa
class (K) (R⊙) 8498˚A 8542˚A 8662˚A Total Hα
3580 K
HD236979 I 3574 524±175 1.87±0.08 3.92±0.10 3.21±0.07 9.01±0.15 1.32±0.09 4
IRC+30465 III 3595 69.9±14.5 1.62±0.05 3.10±0.06 2.83±0.05 7.56±0.09 0.95±0.10 1
IRC+30468 III 3585 60.5±12.8 1.86±0.04 3.87±0.06 3.13±0.05 8.87±0.09 1.00±0.09 1
BD+442051 V 3545 ··· 0.57±0.03 1.47±0.03 1.10±0.03 3.25±0.06 0.35±0.05 2
HD95735 V 3593 0.395±0.013 0.62±0.04 1.34±0.03 1.30±0.03 3.14±0.06 0.36±0.08 3
3650 K
HD14404 I 3647 405±137 2.39±0.08 4.68±0.07 3.82±0.07 10.88±0.12 1.69±0.11 4
HD52005 I 3619 266±82 2.07±0.08 4.91±0.08 3.54±0.07 10.52±0.13 1.54±0.09 4
HR6227 III 3640 ··· 1.67±0.05 3.58±0.06 2.95±0.05 8.16±0.10 1.07±0.10 2
IRC+40022 III 3629 ··· 1.72±0.06 3.63±0.06 2.82±0.05 8.20±0.09 1.02±0.10 1
HD119850 V 3664 0.481±0.040 0.78±0.03 1.65±0.03 1.19±0.04 3.61±0.06 0.50±0.07 3
4050 K
HD13686 I 4054 99±34 2.25±0.07 4.87±0.07 3.84±0.05 10.97±0.11 1.47±0.09 4
HD207991 IIIb 4035 39±6 1.57±0.05 3.60±0.05 2.77±0.04 7.95±0.08 1.19±0.07 4
HR3249 III 4037 ··· 1.67±0.06 4.00±0.06 2.87±0.05 8.54±0.10 1.21±0.07 2
HR7237 III 4075 45.2±5.1 1.78±0.06 3.75±0.05 2.92±0.05 8.45±0.09 1.14±0.09 1
HD157881 V 4030 0.564±0.068 1.22±0.04 2.71±0.04 2.22±0.05 6.15±0.07 0.61±0.06 3
4150 K
HD207119 I 4154 235±92 2.12±0.06 5.16±0.07 3.75±0.07 11.03±0.11 1.53±0.10 4
HR6258 III 4134 71.3±14.4 1.96±0.05 4.02±0.06 3.23±0.05 9.21±0.10 1.31±0.10 1
HR389 III 4144 25.1±2.2 1.54±0.07 3.26±0.06 2.72±0.07 7.52±0.12 1.16±0.09 1
HD88230 V 4156 0.649±0.028 1.11±0.04 2.36±0.03 2.08±0.04 5.55±0.06 0.62±0.04 3
aTeff andstellarradii(whereapplicable) forthesestars aretaken fromfrom(1)vanBelleetal.(1999), (2)Cenarroetal.(2001a), (3)
vanBelleetal.(2009a), and(4)vanBelleetal.(2009b).
bTheluminosityclassofthisstaristakenfromKeenan&McNeil(1989); formorediscussionseeSection3.
